Minimal generating sets for free modules

Minimal Free Resolutions of Homogenized D-modules

Cut-Generating Functions and S-Free Sets

We consider the separation problem for sets X that are inverse images of a given set S by a linear mapping. Classical examples occur in integer programming, complementarity problems and other optimization problems. One would like to generate valid inequalities that cut off some point not lying in X , without reference to the linear mapping. Formulas for such inequalities can be obtained through...

Minimal k-Free Representations of Frequent Sets

Due to the potentially immense amount of frequent sets that can be generated from transactional databases, recent studies have demonstrated the need for concise representations of all frequent sets. These studies resulted in several successful algorithms that only generate a lossless subset of the frequent sets. In this paper, we present a unifying framework encapsulating most known concise rep...

Generating All Minimal Edge Dominating Sets with Incremental-Polynomial Delay

For an arbitrary undirected simple graph G with m edges, we give an algorithm with running time O(m|L|) to generate the set L of all minimal edge dominating sets of G. For bipartite graphs we obtain a better result; we show that their minimal edge dominating sets can be enumerated in time O(m|L|). In fact our results are stronger; both algorithms generate the next minimal edge dominating set wi...

Minimal Separating Sets for

For a Muller automaton only a subset of its states is needed to decide whether a run is accepting or not: The set I the innnitely often visited states can be replaced by the intersection I \ W with a xed set W of states, provided W is large enough to distinguish between accepting and non-accepting loops in the automaton. We call such a subset W a separating set. Whereas the idea was previously ...